# Are Electromagnetic Waves Sinusoidal?

Q:
Are all electromagnetic waves sinusoidal in nature? I know that we can generate any waveshape (say, a square wave) using Fourier series from sinusoidal harmonics. Whenever I see a representation of an EM wave, whether it be the E or B vector, it's always in form of a sinusoid. Is this the fundamental nature of EM waves (derived from mathematical models) or is there another answer? Hopefully my question was clear enough.
- Vaibhav Singh (age 20)
Mumbai, India
A:

Great question. I've heard instructors here get the explanation confused, so it's one that others should see.

As you say, EM waves can follow all sorts of patterns. What's special about sine waves?

In a vacuum, plane waves of any shape propagate keeping the same shape. In materials (e.g. glass or water) the shape of the wave in general changes as it propagates. Each sine-wave component, however, keeps its sinusoidal shape. (I'm assuming that the intensity is low enough that the propagation is linear, typically an excellent approximation.) The shape of a non-sinusoidal wave changes because the sine-wave components propagate at slightly different speeds. So the sine-wave shape is special because it's the shape that doesn't change while propagating through materials.

Closely related to that, it's the single-frequency sinusoidal waves that transfer well-defined quanta of energy to materials. The size of the energy quatum is hf, where f is the frequency and h is the universal Planck's constant. Waves wiith other shapes are made of mixtures of different frequencies and thus have a range of different possible sizes of quantum energy transfers.

Mike W.

(published on 05/23/2018)

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